Use Hubble’s law to connect expansion with the Big Bang
Use the velocity–distance relationship to explain evidence that the Universe is expanding and how this supports the Big Bang theory.
Section 25 · Astronomy and cosmology
A Level · Cambridge International Physics 9702, 2025–2027 syllabus. Topic 25 was checked against Cambridge’s 2028–2030 syllabus; a full reconciliation of every remaining syllabus-year change is still outstanding. Online study supports the theory but cannot replace supervised practical work, full timed assessment or human subject-teacher review.
Before you begin
- Use powers of ten, inverse-square relationships, proportional reasoning and SI units; distinguish wavelength, frequency, speed, flux and luminosity.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What relationship does Hubble’s law describe?
What you will learn
- Explain how redshift supports the idea of an expanding Universe
- Use Hubble’s law v ≈ H₀d
- Explain how expansion leads to the Big Bang theory
Redshifts show that distant galaxies recede
When spectral lines from distant galaxies are redshifted, their wavelengths are longer than their known rest values. In the low-speed model this indicates recession relative to the observer.
A pattern in which distant galaxies generally recede, with more distant galaxies receding faster, is evidence that space is expanding. The relation describes the large-scale pattern; it is not that every individual object must move away from every other object locally.
Hubble’s law links recession speed and distance
Hubble’s law is v ≈ H₀d, where v is recession speed, d is distance and H₀ is the Hubble constant. Use SI units when required: H₀ in s⁻¹, d in metres and v in metres per second.
If the expansion is traced backwards, galaxies were closer together in the past. The Big Bang theory describes an earlier hot, dense state followed by expansion; Hubble’s law connects observed recession with that expanding-Universe picture.
Pause and explain
What does extrapolating cosmic expansion backwards suggest?
Worked example
A galaxy is 3.0 × 10²⁴ m away. Use H₀ = 2.3 × 10⁻¹⁸ s⁻¹ to estimate its recession speed.
Show the worked solution
- Use v ≈ H₀d.
- v = 2.3 × 10⁻¹⁸ × 3.0 × 10²⁴ m s⁻¹.
- v = 6.9 × 10⁶ m s⁻¹.
Answer 6.9 × 10⁶ m s⁻¹.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Use H₀ = 2.0 × 10⁻¹⁸ s⁻¹ and d = 5.0 × 10²³ m to estimate v.
Give me a hint
Multiply the Hubble constant by distance.
Compare my reasoning
- v ≈ H₀d.
- v = 2.0 × 10⁻¹⁸ × 5.0 × 10²³ m s⁻¹.
- v = 1.0 × 10⁶ m s⁻¹.
1.0 × 10⁶ m s⁻¹.
Look for these in your work
- Uses the correct law
- Uses SI units
- Reports speed units
Galaxy A is twice as far away as galaxy B. According to Hubble’s law, how do their recession speeds compare?
Give me a hint
Assume the same Hubble constant and apply v = H₀d.
Compare my reasoning
- For both galaxies, v is proportional to d.
- If dA = 2dB, then vA = H₀(2dB).
- Therefore vA = 2vB.
Galaxy A’s recession speed is twice galaxy B’s in the Hubble-law model.
Look for these in your work
- Uses the same H₀
- Applies direct proportionality
- States the speed ratio
Explain the reasoning from observed galaxy redshifts to the Big Bang theory without claiming that one measurement proves the whole theory.
Give me a hint
Connect the observations, expansion model and backward extrapolation.
Compare my reasoning
- Distant-galaxy spectral lines are observed at longer wavelengths, indicating redshift and recession in the low-speed model.
- Hubble’s law links recession speed to distance, supporting large-scale expansion.
- Tracing that expansion backwards suggests an earlier hot, dense state; this is evidence that supports the Big Bang theory, alongside other evidence.
Redshift and Hubble’s law support an expanding Universe; extrapolating expansion backwards suggests an earlier hot, dense state described by the Big Bang theory.
Look for these in your work
- Connects spectral shifts to recession
- Uses Hubble’s relation as evidence for expansion
- Describes the backward inference without overstating what one observation proves
Common mistakes
- Using H₀ as a speed rather than an inverse time
- Mixing distance units with an H₀ value in incompatible units
- Claiming Hubble’s law says every nearby object must recede from the observer
What can you explain now?
What relationship does Hubble’s law describe?
Compare with the explanation
Recession speed proportional to distance
The law is v ≈ H₀d.
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Make it stick
How does Hubble’s law connect a galaxy’s distance with the evidence for cosmic expansion?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.